Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
public class A {
	Scanner sc = new Scanner(System.in);
	void doIt()
	{
		long N = sc.nextLong();
		ArrayList<Long> tri = new ArrayList<Long>();
		for(long k = 1; ; k++) {
			long n = k * (k + (long)1) / (long)2;
			if(n > N) break;
			tri.add(n);
		}
		//System.out.println(tri.size());
		int small = 0, large = tri.size() - 1;
		while(small <= large) {
			long sum = tri.get(small) + tri.get(large);
			if(sum == N) {
				System.out.println("YES");
				return;
			}
			else if(sum > N) large--;
			else small++;
		}
		System.out.println("NO");
	}
	
	public static void main(String[] args) {
		new A().doIt();
	}

}